O Macmillan Learning Industrial processes often require the damping of vibrations. Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of k = 47500 N/m. This workbench is used when creating products that involve highly unstable chemicals. According to specifications, the acceleration of the manufacturing equipment must be held to less than 21.6 m/s² for the manufacturing process to proceed safely. The amplitudes of vibrations are expected to remain under 0.592 mm throughout. Given that the workbench and maufacturing equipment have a combined mass of m= 5.95 kg, find the maximum acceleration amax expected of the equipment and workbench. Ignore the mass of the springs. Omax = Does the workbench meet the specifications for acceleration? yes no m/s² An engineer decides to damp the oscillations by applying one shock absorber to each spring. These shock absorbers apply a that oppores the motion of the bench. For proper damping, the engineer decides that the F

O Macmillan Learning Industrial processes often require the damping of vibrations. Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of k = 47500 N/m. This workbench is used when creating products that involve highly unstable chemicals. According to specifications, the acceleration of the manufacturing equipment must be held to less than 21.6 m/s² for the manufacturing process to proceed safely. The amplitudes of vibrations are expected to remain under 0.592 mm throughout. Given that the workbench and maufacturing equipment have a combined mass of m= 5.95 kg, find the maximum acceleration amax expected of the equipment and workbench. Ignore the mass of the springs. Omax = Does the workbench meet the specifications for acceleration? yes no m/s² An engineer decides to damp the oscillations by applying one shock absorber to each spring. These shock absorbers apply a that oppores the motion of the bench. For proper damping, the engineer decides that the F

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Description: Macmillan LearningIndustrial processes often require the damping of vibrations.Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner ofthe workbench and exhibiting a force consta

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

Macmillan Learning
Industrial processes often require the damping of vibrations.
Consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of
the workbench and exhibiting a force constant of k = 47500 N/m. This workbench is used when creating products that involve
highly unstable chemicals. According to specifications, the acceleration of the manufacturing equipment must be held to less
than 21.6 m/s² for the manufacturing process to proceed safely. The amplitudes of vibrations are expected to remain under
0.592 mm throughout. Given that the workbench and maufacturing equipment have a combined mass of m= 5.95 kg, find the
maximum acceleration amax expected of the equipment and workbench. Ignore the mass of the springs.
@max =
Does the workbench meet the specifications for acceleration?
yes
no
m/s²
An engineer decides to damp the oscillations by applying one shock absorber to each spring. These shock absorbers apply a
velocity-dependent drag force F = -bu that opposes the motion of the bench. For proper damping, the engineer decides that the
motion of the bench should drop to half-amplitude within 0.479 s. In other words, within 0.479 s, the amplitude of motion
should drop by a factor of one half. When purchasing shock absorbers, what damping coefficient b should the engineer specify
to the industrial equipment supplier? Assume that the oscillations are underdamped.
b =
kg/s

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